Question - Financial Calculation for University Printery Modules
Solution:
The image contains a mathematical problem that requires the creation of a formula based on given charging criteria and then using that formula to calculate specific costs. Here is the problem as shown in the image:"A University printery produces student modules. The printery charges for a module depending on the size of the module, the types of cover and binding used, and the number of books in a print run. The charging formula is as follows: Charge 4 toea per page for paper and collating, and 20 toea per page for cardboard covers. Next add a charge of 5 toea per written page for printing, labour, and other page related costs; and charge K5.00 per printed page for masters that can be used for a minimum of 500 copies. Finally add 20% to the calculated cost to cover for labour costs.(a) Find a formula for a module that has P paper pages, and C cardboard covers, and is bound. Each module has 2 pages of print and the print run is 500 modules. (b) Use the formula to find the charges for a module that has 60 pages, 2 covers, and is bound. Each module has 2 pages of print and the print run is 300 modules."Let's first tackle part (a) to create a formula.Cost per paper page (for paper and collating): 4 toeaCost per cardboard cover page: 20 toeaCost per written page (for printing, labour, and other costs): 5 toeaCost per printed page for masters: K5.00 (since it can be used for a minimum of 500 copies, there is no need to multiply by the number of modules for this cost)Let's create the cost formula:Cost = (P * 4 toea) + (C * 20 toea) + (P * 5 toea) + (2 * K5.00) + 20% of the cost.To simplify:Cost = 0.09P + 0.20C + 10 + 0.20(Cost)We can't have cost on both sides of the equation, so we need to isolate it. Let's factor out the cost on the right side of the equation:Cost = 0.09P + 0.20C + 101.20 * Cost = 0.09P + 0.20C + 10Cost = (0.09P + 0.20C + 10) / 1.20.This represents the total cost to produce one module. Now let's use this formula for part (b).For part (b), we have:P = 60 pages,C = 2 covers.Plugging the numbers into the formula, we get:Cost = (0.09 * 60 + 0.20 * 2 + 10) / 1.20Cost = (5.40 + 0.40 + 10) / 1.20Cost = 15.80 / 1.20Cost = 13.1667.So the cost per module with 60 pages, 2 covers, and bound, with 2 pages of print for a print run of 300 modules, is approximately K13.17.
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